English

A Sparse $Z_2$ Chain Complex Without a Sparse Lift

Quantum Physics 2025-10-01 v2 Geometric Topology

Abstract

We construct a sparse Z2Z_2 chain complex (with three different degrees, so that it corresponds to a quantum code) which does not admit a sparse lift to the integers, answering a question in Ref. 1.

Cite

@article{arxiv.2509.22998,
  title  = {A Sparse $Z_2$ Chain Complex Without a Sparse Lift},
  author = {Matthew B. Hastings},
  journal= {arXiv preprint arXiv:2509.22998},
  year   = {2025}
}

Comments

6 pages, 0 figures; v2 minor typos

R2 v1 2026-07-01T06:00:02.698Z